Question: Kevin is 2 times as old as Vanessa. Eighteen years ago, Kevin was 8 times as old as Vanessa. How old is Vanessa now?
Solution: We can use the given information to write down two equations that describe the ages of Kevin and Vanessa. Let Kevin's current age be $k$ and Vanessa's current age be $v$ The information in the first sentence can be expressed in the following equation: $k = 2v$ Eighteen years ago, Kevin was $k - 18$ years old, and Vanessa was $v - 18$ years old. The information in the second sentence can be expressed in the following equation: $k - 18 = 8(v - 18)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $v$ , it might be easiest to use our first equation for $k$ and substitute it into our second equation. Our first equation is: $k = 2v$ . Substituting this into our second equation, we get: $2v$ $-$ $18 = 8(v - 18)$ which combines the information about $v$ from both of our original equations. Simplifying the right side of this equation, we get: $2 v - 18 = 8 v - 144$ Solving for $v$ , we get: $6 v = 126.$ $v = 21$.